Consider the following model which therefore generalizes model

(iii) of Section 4.7. A sample of ni subjects is obtained from class Ai(i = 1,..., a), the samples from different classes being independent. If Yi,j is the number of subjects from the ith sample belonging to Bj(j = 1,..., b), the joint distribution of

(Yi,1,..., Yi,b) is multinomial, say,

M(ni; p1|i,..., pb|i) .
Determine the likelihood ratio statistic for testing the hypothesis of homogeneity that the vector (p1|i,..., pb|i)is independent of i, and specify its asymptotic distribution.